Pineapple

Introduction

The purpose of this page will be to show how to play the initial hand decision in the poker game Pineapple. For those who don't know, Pineapple is played like Texas Hold 'Em, except the player is dealt three hole cards and must discard one after an initial round of betting and before the flop. This is not to be confused with Crazy Pineapple, where the discard decision is made just before the Turn, or Lazy Pineapple, where the player holds onto all three throughout the game.

This page only endeavors to cover the decision on which card to discard and the power of each starting hand. Through the page you will find expected value statistics. This is how much the player can expect to get back based on a one unit ante. For example, an expected return of 1.000 would be breaking even.

A term you will see a lot on this page is "penalty," which I get from video poker. It means discarding a card which could be potentially helpful. To be specific, a rank penalty is the card you discard after being dealt a three of a kind. This is a heartbreaking hand to get in Pineapple, because you must throw one of the cards away. Not only does this lower the value of your hand, but there is one less card in the deck to improve your pair. Suit penalties are much more common. If your discard is suited to one of the cards you're keeping, it lowers the chances of making a flush. The ideal situation is no penalty of either kind.

Assumptions

This page assumes a six-player game where nobody ever folds or raises. Each player antes one unit and the best hand at the end wins.

Three of a Kind

The strategy for being dealt a three of a kind is simple — hold any two cards.

The following table shows the expected return of holding any two cards when dealt a three of a kind.

Dealt Three of Kind

Rank

ExpectedReturn

A

2.425

K

1.925

Q

1.563

J

1.297

10

1.084

9

0.899

8

0.777

7

0.687

6

0.624

5

0.571

4

0.521

3

0.483

2

0.448

Pair without Suit Penalty

The strategy with any pair is simple — hold the pair.

The following table shows the expected return for both viable ways to play when dealt a pair and a singleton, when the singleton is not suited to either of the cards in the pair. Either you keep the pair or the singleton and either card in the pair. As you can see, the table shows holding the pair is always has the greater expected value, by far.

Dealt Three of Kind

Rank

Singleton

Pair

TwoSingletons

A

K

2.708

1.289

A

Q

2.719

1.159

A

J

2.729

1.059

A

10

2.740

0.985

A

9

2.739

0.827

A

8

2.734

0.785

A

7

2.736

0.753

A

6

2.737

0.722

A

5

2.734

0.777

A

4

2.719

0.753

A

3

2.701

0.728

A

2

2.674

0.694

K

A

2.392

1.276

K

Q

2.224

1.082

K

J

2.237

0.999

K

10

2.245

0.936

K

9

2.246

0.784

K

8

2.243

0.683

K

7

2.245

0.661

K

6

2.247

0.641

K

5

2.245

0.622

K

4

2.234

0.603

K

3

2.219

0.582

K

2

2.201

0.562

Q

A

1.999

1.147

Q

K

1.994

1.080

Q

J

1.865

0.975

Q

10

1.880

0.920

Q

9

1.876

0.773

Q

8

1.877

0.676

Q

7

1.879

0.592

Q

6

1.881

0.580

Q

5

1.880

0.564

Q

4

1.873

0.543

Q

3

1.859

0.525

Q

2

1.847

0.509

J

A

1.702

1.052

J

K

1.696

0.998

J

Q

1.696

0.971

J

10

1.601

0.931

J

9

1.600

0.792

J

8

1.599

0.696

J

7

1.601

0.610

J

6

1.603

0.537

J

5

1.606

0.523

J

4

1.597

0.506

J

3

1.591

0.488

J

2

1.582

0.474

10

A

1.466

0.980

10

K

1.465

0.934

10

Q

1.464

0.918

10

J

1.465

0.926

10

9

1.388

0.823

10

8

1.388

0.734

10

7

1.388

0.650

10

6

1.394

0.569

10

5

1.394

0.497

10

4

1.388

0.481

10

3

1.383

0.465

10

2

1.377

0.453

9

A

1.284

0.815

9

K

1.288

0.767

9

Q

1.286

0.755

9

J

1.287

0.769

9

10

1.288

0.803

9

8

1.223

0.720

9

7

1.224

0.663

9

6

1.226

0.591

9

5

1.226

0.513

9

4

1.225

0.438

9

3

1.221

0.426

9

2

1.216

0.414

8

A

1.159

0.774

8

K

1.159

0.669

8

Q

1.160

0.655

8

J

1.163

0.672

8

10

1.162

0.708

8

9

1.159

0.708

8

7

1.110

0.688

8

6

1.110

0.635

8

5

1.112

0.560

8

4

1.109

0.479

8

3

1.108

0.407

8

2

1.103

0.398

7

A

1.059

0.739

7

K

1.063

0.649

7

Q

1.066

0.577

7

J

1.068

0.584

7

10

1.069

0.620

7

9

1.062

0.643

7

8

1.065

0.673

7

6

1.021

0.661

7

5

1.027

0.609

7

4

1.024

0.532

7

3

1.024

0.451

7

2

1.022

0.383

6

A

0.989

0.713

6

K

0.994

0.629

6

Q

0.994

0.564

6

J

1.000

0.515

6

10

1.000

0.541

6

9

0.997

0.568

6

8

0.996

0.617

6

7

0.995

0.650

6

5

0.962

0.643

6

4

0.961

0.584

6

3

0.959

0.508

6

2

0.960

0.429

5

A

0.931

0.775

5

K

0.935

0.613

5

Q

0.937

0.552

5

J

0.939

0.507

5

10

0.943

0.476

5

9

0.940

0.494

5

8

0.940

0.543

5

7

0.940

0.597

5

6

0.937

0.635

5

4

0.911

0.633

5

3

0.906

0.571

5

2

0.909

0.500

4

A

0.882

0.749

4

K

0.887

0.590

4

Q

0.891

0.530

4

J

0.891

0.487

4

10

0.893

0.458

4

9

0.894

0.420

4

8

0.891

0.460

4

7

0.895

0.514

4

6

0.891

0.570

4

5

0.891

0.623

4

3

0.866

0.534

4

2

0.864

0.478

3

A

0.843

0.723

3

K

0.848

0.568

3

Q

0.850

0.509

3

J

0.852

0.467

3

10

0.853

0.440

3

9

0.851

0.404

3

8

0.854

0.386

3

7

0.853

0.429

3

6

0.853

0.488

3

5

0.851

0.556

3

4

0.851

0.525

3

2

0.829

0.440

2

A

0.816

0.683

2

K

0.818

0.544

2

Q

0.823

0.489

2

J

0.823

0.445

2

10

0.826

0.421

2

9

0.824

0.386

2

8

0.823

0.374

2

7

0.826

0.360

2

6

0.824

0.403

2

5

0.824

0.478

2

4

0.823

0.459

2

3

0.821

0.431

Pair with Suit Penalty

The strategy with any pair is simple — hold the pair.

The following table shows the expected return for all three possible plays when dealt a pair and a singleton, when the singleton is suited to one of the cards in the pair. Being suited is bad, because it lowers the chance of forming a flush when holding the pair. As you can see, the table shows holding the pair is always has the greatest expected value, by far.

Dealt Three of Kind

Rank

Singleton

Pair

SuitedSingletons

UnsuitedSingletons

A

K

2.678

1.496

1.272

A

Q

2.690

1.379

1.143

A

J

2.704

1.287

1.045

A

10

2.714

1.224

0.975

A

9

2.712

1.080

0.820

A

8

2.707

1.042

0.777

A

7

2.708

1.013

0.745

A

6

2.710

0.986

0.713

A

5

2.708

1.037

0.768

A

4

2.691

1.014

0.744

A

3

2.672

0.995

0.722

A

2

2.650

0.962

0.687

K

A

2.378

1.485

1.250

K

Q

2.205

1.300

1.072

K

J

2.214

1.221

0.986

K

10

2.222

1.168

0.926

K

9

2.223

1.026

0.773

K

8

2.224

0.936

0.675

K

7

2.224

0.915

0.652

K

6

2.226

0.899

0.635

K

5

2.226

0.884

0.618

K

4

2.210

0.863

0.594

K

3

2.198

0.846

0.576

K

2

2.181

0.828

0.557

Q

A

1.984

1.367

1.119

Q

K

1.980

1.295

1.057

Q

J

1.849

1.192

0.961

Q

10

1.858

1.145

0.911

Q

9

1.856

1.007

0.762

Q

8

1.858

0.921

0.668

Q

7

1.865

0.848

0.587

Q

6

1.858

0.834

0.573

Q

5

1.860

0.822

0.558

Q

4

1.854

0.803

0.539

Q

3

1.841

0.787

0.521

Q

2

1.828

0.769

0.503

J

A

1.686

1.280

1.024

J

K

1.687

1.221

0.975

J

Q

1.684

1.189

0.953

J

10

1.587

1.150

0.922

J

9

1.582

1.019

0.781

J

8

1.584

0.936

0.689

J

7

1.585

0.856

0.603

J

6

1.592

0.784

0.529

J

5

1.589

0.777

0.518

J

4

1.584

0.758

0.500

J

3

1.576

0.744

0.483

J

2

1.566

0.730

0.468

10

A

1.459

1.220

0.957

10

K

1.454

1.169

0.917

10

Q

1.456

1.144

0.901

10

J

1.456

1.145

0.912

10

9

1.371

1.048

0.816

10

8

1.372

0.962

0.724

10

7

1.374

0.885

0.641

10

6

1.378

0.813

0.562

10

5

1.383

0.744

0.490

10

4

1.374

0.733

0.476

10

3

1.369

0.717

0.460

10

2

1.364

0.703

0.447

9

A

1.276

1.068

0.792

9

K

1.275

1.011

0.746

9

Q

1.278

0.992

0.737

9

J

1.280

0.999

0.754

9

10

1.280

1.027

0.789

9

8

1.212

0.949

0.713

9

7

1.212

0.896

0.656

9

6

1.213

0.827

0.583

9

5

1.214

0.757

0.507

9

4

1.215

0.688

0.433

9

3

1.210

0.676

0.422

9

2

1.205

0.661

0.407

8

A

1.148

1.029

0.748

8

K

1.149

0.923

0.652

8

Q

1.154

0.902

0.639

8

J

1.155

0.911

0.658

8

10

1.153

0.939

0.695

8

9

1.150

0.934

0.694

8

7

1.099

0.915

0.678

8

6

1.101

0.866

0.627

8

5

1.102

0.799

0.556

8

4

1.100

0.722

0.474

8

3

1.097

0.653

0.401

8

2

1.094

0.644

0.394

7

A

1.053

1.000

0.715

7

K

1.054

0.904

0.627

7

Q

1.058

0.829

0.560

7

J

1.059

0.831

0.570

7

10

1.062

0.862

0.612

7

9

1.057

0.878

0.633

7

8

1.054

0.902

0.663

7

6

1.016

0.889

0.655

7

5

1.016

0.841

0.605

7

4

1.014

0.763

0.524

7

3

1.014

0.689

0.445

7

2

1.013

0.625

0.379

6

A

0.984

0.975

0.688

6

K

0.985

0.888

0.610

6

Q

0.988

0.820

0.549

6

J

0.991

0.768

0.503

6

10

0.992

0.785

0.529

6

9

0.988

0.808

0.558

6

8

0.988

0.848

0.606

6

7

0.986

0.877

0.641

6

5

0.953

0.868

0.637

6

4

0.952

0.811

0.577

6

3

0.950

0.737

0.500

6

2

0.949

0.663

0.424

5

A

0.924

1.037

0.752

5

K

0.930

0.876

0.596

5

Q

0.931

0.811

0.538

5

J

0.933

0.760

0.494

5

10

0.939

0.725

0.464

5

9

0.936

0.740

0.484

5

8

0.931

0.783

0.535

5

7

0.933

0.827

0.587

5

6

0.930

0.859

0.626

5

4

0.900

0.855

0.627

5

3

0.900

0.798

0.568

5

2

0.902

0.727

0.496

4

A

0.876

1.011

0.726

4

K

0.880

0.856

0.573

4

Q

0.884

0.792

0.516

4

J

0.885

0.742

0.473

4

10

0.886

0.712

0.449

4

9

0.888

0.670

0.410

4

8

0.887

0.704

0.452

4

7

0.886

0.749

0.505

4

6

0.884

0.796

0.561

4

5

0.883

0.848

0.618

4

3

0.859

0.759

0.530

4

2

0.858

0.704

0.474

3

A

0.839

0.989

0.699

3

K

0.840

0.834

0.549

3

Q

0.846

0.771

0.494

3

J

0.847

0.724

0.453

3

10

0.849

0.694

0.429

3

9

0.846

0.656

0.394

3

8

0.848

0.634

0.378

3

7

0.846

0.669

0.421

3

6

0.846

0.721

0.481

3

5

0.845

0.781

0.549

3

4

0.843

0.749

0.518

3

2

0.822

0.667

0.436

2

A

0.811

0.954

0.660

2

K

0.813

0.813

0.526

2

Q

0.816

0.751

0.472

2

J

0.817

0.707

0.434

2

10

0.819

0.675

0.410

2

9

0.816

0.640

0.377

2

8

0.819

0.623

0.366

2

7

0.818

0.603

0.352

2

6

0.816

0.641

0.397

2

5

0.819

0.704

0.470

2

4

0.817

0.687

0.454

2

3

0.815

0.660

0.427

Three Suited Singletons

The following table shows the expected return for all three possible plays when dealt three suited singletons. Most of the time, the best play is to discard the lowest one. However, if all the cards are low, and the lowest two are close together and the highest not, then sometimes you go for the straight by playing the two lowest.

Three Suited Singletons

Hand

Discard

ExpectedReturnMiddle and High

ExpectedReturnLow and High

ExpectedReturnLow and Middle

A-K-Q

Q

1.541

1.443

1.405

A-K-J

J

1.550

1.325

1.305

A-K-10

10

1.550

1.240

1.230

A-K-9

9

1.559

1.102

1.093

A-K-8

8

1.548

1.053

0.988

A-K-7

7

1.557

1.016

0.967

A-K-6

6

1.551

0.986

0.942

A-K-5

5

1.559

1.031

0.924

A-K-4

4

1.554

1.012

0.903

A-K-3

3

1.543

0.987

0.885

A-K-2

2

1.536

0.955

0.865

A-Q-J

J

1.402

1.325

1.245

A-Q-10

10

1.399

1.238

1.185

A-Q-9

9

1.415

1.099

1.055

A-Q-8

8

1.414

1.054

0.957

A-Q-7

7

1.412

1.018

0.885

A-Q-6

6

1.417

0.987

0.870

A-Q-5

5

1.418

1.032

0.852

A-Q-4

4

1.411

1.009

0.831

A-Q-3

3

1.405

0.987

0.814

A-Q-2

2

1.398

0.954

0.800

A-J-10

10

1.298

1.238

1.174

A-J-9

9

1.307

1.099

1.048

A-J-8

8

1.306

1.052

0.952

A-J-7

7

1.305

1.021

0.877

A-J-6

6

1.307

0.990

0.813

A-J-5

5

1.310

1.028

0.798

A-J-4

4

1.306

1.013

0.780

A-J-3

3

1.305

0.989

0.767

A-J-2

2

1.295

0.956

0.752

A-10-9

9

1.228

1.099

1.068

A-10-8

8

1.229

1.054

0.979

A-10-7

7

1.227

1.015

0.895

A-10-6

6

1.233

0.992

0.828

A-10-5

5

1.234

1.037

0.764

A-10-4

4

1.229

1.010

0.747

A-10-3

3

1.225

0.990

0.735

A-10-2

2

1.223

0.959

0.722

A-9-8

8

1.078

1.046

0.969

A-9-7

7

1.079

1.015

0.915

A-9-6

6

1.079

0.985

0.845

A-9-5

5

1.083

1.031

0.779

A-9-4

4

1.077

1.010

0.709

A-9-3

3

1.079

0.989

0.704

A-9-2

2

1.070

0.951

0.686

A-8-7

7

1.032

1.010

0.926

A-8-6

6

1.031

0.982

0.880

A-8-5

5

1.034

1.026

0.814

A-8-4

4

1.037

1.011

0.739

A-8-3

3

1.034

0.990

0.679

A-8-2

2

1.025

0.953

0.670

A-7-6

6

0.997

0.978

0.904

A-7-5

7

1.000

1.028

0.854

A-7-4

7

1.003

1.009

0.783

A-7-3

3

0.998

0.988

0.710

A-7-2

2

0.996

0.962

0.650

A-6-5

6

0.971

1.025

0.883

A-6-4

6

0.973

1.005

0.829

A-6-3

6

0.970

0.986

0.762

A-6-2

2

0.969

0.961

0.688

A-5-4

4

1.003

0.990

0.855

A-5-3

3

1.003

0.971

0.800

A-5-2

2

1.001

0.944

0.731

A-4-3

3

0.981

0.967

0.766

A-4-2

2

0.982

0.941

0.713

A-3-2

2

0.959

0.937

0.686

K-Q-J

J

1.300

1.239

1.234

K-Q-10

10

1.303

1.166

1.170

K-Q-9

9

1.316

1.030

1.045

K-Q-8

8

1.324

0.950

0.961

K-Q-7

7

1.321

0.923

0.878

K-Q-6

6

1.324

0.904

0.867

K-Q-5

5

1.326

0.886

0.852

K-Q-4

4

1.321

0.868

0.836

K-Q-3

3

1.316

0.844

0.816

K-Q-2

2

1.309

0.829

0.801

K-J-10

10

1.216

1.170

1.159

K-J-9

9

1.227

1.033

1.038

K-J-8

8

1.239

0.953

0.964

K-J-7

7

1.239

0.930

0.880

K-J-6

6

1.235

0.906

0.813

K-J-5

5

1.239

0.891

0.804

K-J-4

4

1.232

0.864

0.780

K-J-3

3

1.227

0.849

0.769

K-J-2

2

1.223

0.830

0.752

K-10-9

9

1.156

1.027

1.046

K-10-8

8

1.172

0.952

0.981

K-10-7

7

1.170

0.927

0.899

K-10-6

6

1.174

0.907

0.825

K-10-5

5

1.173

0.888

0.763

K-10-4

4

1.169

0.867

0.747

K-10-3

3

1.167

0.851

0.736

K-10-2

2

1.164

0.831

0.721

K-9-8

8

1.017

0.946

0.976

K-9-7

7

1.023

0.925

0.914

K-9-6

6

1.018

0.901

0.845

K-9-5

5

1.023

0.888

0.779

K-9-4

4

1.023

0.869

0.714

K-9-3

3

1.016

0.849

0.701

K-9-2

2

1.014

0.832

0.689

K-8-7

K

0.931

0.917

0.933

K-8-6

6

0.931

0.897

0.882

K-8-5

5

0.935

0.884

0.816

K-8-4

4

0.934

0.866

0.745

K-8-3

3

0.930

0.848

0.682

K-8-2

2

0.927

0.826

0.675

K-7-6

6

0.906

0.894

0.901

K-7-5

5

0.908

0.880

0.857

K-7-4

4

0.908

0.866

0.785

K-7-3

3

0.907

0.848

0.714

K-7-2

2

0.905

0.833

0.655

K-6-5

5

0.883

0.874

0.880

K-6-4

4

0.883

0.859

0.824

K-6-3

3

0.888

0.846

0.760

K-6-2

2

0.886

0.831

0.689

K-5-4

K

0.868

0.856

0.871

K-5-3

3

0.870

0.843

0.817

K-5-2

2

0.868

0.827

0.750

K-4-3

3

0.850

0.840

0.784

K-4-2

2

0.847

0.822

0.728

K-3-2

2

0.828

0.818

0.699

Q-J-10

10

1.156

1.119

1.142

Q-J-9

9

1.174

0.995

1.022

Q-J-8

8

1.181

0.914

0.948

Q-J-7

7

1.199

0.859

0.881

Q-J-6

6

1.191

0.842

0.810

Q-J-5

5

1.198

0.826

0.801

Q-J-4

4

1.190

0.806

0.781

Q-J-3

3

1.186

0.786

0.763

Q-J-2

2

1.182

0.775

0.755

Q-10-9

9

1.114

0.993

1.034

Q-10-8

8

1.126

0.912

0.963

Q-10-7

7

1.141

0.854

0.900

Q-10-6

6

1.143

0.841

0.824

Q-10-5

5

1.139

0.825

0.763

Q-10-4

4

1.140

0.808

0.746

Q-10-3

3

1.140

0.793

0.734

Q-10-2

2

1.134

0.779

0.725

Q-9-8

8

0.981

0.911

0.960

Q-9-7

7

0.998

0.846

0.915

Q-9-6

6

0.997

0.840

0.841

Q-9-5

5

0.997

0.826

0.777

Q-9-4

4

0.999

0.810

0.712

Q-9-3

3

0.997

0.793

0.704

Q-9-2

2

0.993

0.775

0.692

Q-8-7

Q

0.906

0.843

0.938

Q-8-6

6

0.910

0.833

0.883

Q-8-5

5

0.909

0.821

0.818

Q-8-4

4

0.909

0.805

0.742

Q-8-3

3

0.908

0.792

0.682

Q-8-2

2

0.906

0.773

0.672

Q-7-6

Q

0.837

0.833

0.913

Q-7-5

Q

0.836

0.816

0.860

Q-7-4

4

0.839

0.806

0.788

Q-7-3

3

0.840

0.788

0.715

Q-7-2

2

0.832

0.773

0.655

Q-6-5

Q

0.821

0.813

0.883

Q-6-4

Q

0.826

0.801

0.830

Q-6-3

3

0.823

0.786

0.761

Q-6-2

2

0.824

0.774

0.690

Q-5-4

Q

0.808

0.794

0.873

Q-5-3

Q

0.806

0.781

0.817

Q-5-2

2

0.808

0.770

0.750

Q-4-3

3

0.789

0.782

0.785

Q-4-2

2

0.789

0.768

0.732

Q-3-2

2

0.777

0.767

0.703

J-10-9

9

1.094

0.979

1.021

J-10-8

8

1.112

0.911

0.955

J-10-7

7

1.122

0.839

0.886

J-10-6

6

1.140

0.792

0.829

J-10-5

5

1.136

0.781

0.762

J-10-4

4

1.132

0.763

0.745

J-10-3

3

1.132

0.749

0.730

J-10-2

2

1.129

0.734

0.721

J-9-8

8

0.974

0.903

0.946

J-9-7

7

0.991

0.841

0.907

J-9-6

6

1.006

0.791

0.853

J-9-5

5

1.000

0.778

0.777

J-9-4

4

1.000

0.764

0.711

J-9-3

3

0.997

0.744

0.700

J-9-2

2

0.998

0.731

0.689

J-8-7

J

0.902

0.836

0.928

J-8-6

6

0.917

0.785

0.888

J-8-5

5

0.920

0.776

0.817

J-8-4

4

0.918

0.758

0.741

J-8-3

3

0.913

0.743

0.679

J-8-2

2

0.916

0.730

0.672

J-7-6

J

0.836

0.781

0.913

J-7-5

J

0.838

0.771

0.858

J-7-4

4

0.839

0.756

0.786

J-7-3

3

0.837

0.739

0.710

J-7-2

2

0.839

0.734

0.655

J-6-5

J

0.778

0.773

0.890

J-6-4

J

0.775

0.756

0.833

J-6-3

3

0.775

0.740

0.766

J-6-2

2

0.776

0.732

0.691

J-5-4

J

0.765

0.756

0.875

J-5-3

J

0.765

0.738

0.814

J-5-2

2

0.762

0.725

0.749

J-4-3

J

0.751

0.743

0.788

J-4-2

2

0.749

0.729

0.731

J-3-2

2

0.734

0.725

0.702

10-9-8

8

0.982

0.915

0.929

10-9-7

7

0.997

0.850

0.887

10-9-6

6

1.007

0.792

0.833

10-9-5

5

1.025

0.744

0.780

10-9-4

4

1.023

0.733

0.710

10-9-3

3

1.017

0.715

0.696

10-9-2

2

1.018

0.705

0.687

10-8-7

7

0.916

0.852

0.911

10-8-6

6

0.932

0.792

0.873

10-8-5

5

0.942

0.743

0.817

10-8-4

4

0.938

0.729

0.737

10-8-3

3

0.943

0.722

0.680

10-8-2

2

0.938

0.705

0.670

10-7-6

10

0.853

0.788

0.901

10-7-5

5

0.863

0.736

0.858

10-7-4

4

0.864

0.728

0.783

10-7-3

3

0.867

0.717

0.709

10-7-2

2

0.865

0.709

0.654

10-6-5

10

0.793

0.738

0.892

10-6-4

10

0.792

0.727

0.827

10-6-3

3

0.794

0.714

0.762

10-6-2

2

0.790

0.700

0.687

10-5-4

10

0.733

0.724

0.876

10-5-3

10

0.732

0.711

0.822

10-5-2

10

0.733

0.700

0.753

10-4-3

10

0.718

0.709

0.784

10-4-2

10

0.720

0.700

0.734

10-3-2

2

0.706

0.699

0.702

9-8-7

7

0.898

0.856

0.897

9-8-6

6

0.910

0.800

0.857

9-8-5

5

0.925

0.748

0.806

9-8-4

4

0.941

0.698

0.746

9-8-3

3

0.934

0.682

0.677

9-8-2

2

0.929

0.673

0.669

9-7-6

9

0.858

0.800

0.886

9-7-5

5

0.869

0.744

0.847

9-7-4

4

0.883

0.689

0.788

9-7-3

3

0.881

0.680

0.710

9-7-2

2

0.879

0.670

0.651

9-6-5

9

0.802

0.743

0.881

9-6-4

9

0.816

0.690

0.831

9-6-3

3

0.814

0.680

0.759

9-6-2

2

0.816

0.668

0.688

9-5-4

9

0.748

0.689

0.882

9-5-3

9

0.746

0.676

0.817

9-5-2

9

0.750

0.669

0.752

9-4-3

9

0.683

0.676

0.792

9-4-2

9

0.685

0.668

0.736

9-3-2

9

0.672

0.666

0.704

8-7-6

8

0.864

0.825

0.869

8-7-5

5

0.875

0.772

0.832

8-7-4

4

0.890

0.712

0.773

8-7-3

3

0.907

0.665

0.715

8-7-2

2

0.902

0.657

0.653

8-6-5

8

0.831

0.771

0.866

8-6-4

4

0.842

0.710

0.816

8-6-3

3

0.855

0.661

0.762

8-6-2

2

0.855

0.654

0.689

8-5-4

8

0.775

0.706

0.864

8-5-3

8

0.791

0.658

0.823

8-5-2

2

0.786

0.652

0.748

8-4-3

8

0.717

0.657

0.796

8-4-2

8

0.717

0.652

0.733

8-3-2

8

0.653

0.652

0.709

7-6-5

7

0.841

0.802

0.849

7-6-4

4

0.852

0.740

0.800

7-6-3

3

0.868

0.683

0.746

7-6-2

2

0.882

0.637

0.693

7-5-4

7

0.804

0.742

0.852

7-5-3

3

0.819

0.680

0.808

7-5-2

2

0.836

0.636

0.753

7-4-3

7

0.754

0.685

0.784

7-4-2

2

0.769

0.637

0.740

7-3-2

7

0.694

0.639

0.715

6-5-4

6

0.823

0.777

0.832

6-5-3

3

0.838

0.720

0.790

6-5-2

2

0.851

0.665

0.738

6-4-3

3

0.782

0.718

0.762

6-4-2

2

0.796

0.662

0.720

6-3-2

2

0.732

0.661

0.696

5-4-3

3

0.810

0.759

0.742

5-4-2

2

0.826

0.711

0.700

5-3-2

2

0.772

0.709

0.677

4-3-2

2

0.738

0.691

0.673

Three Unsuited Singletons

The following table shows the expected return for all three possible plays when dealt three unsuited singletons. Most of the time, the best play is to discard the lowest one. However, if all the cards are low, and the lowest two are close together and the highest not, then sometimes you go for the straight by playing the two lowest.

Three Unsuited Singletons

Hand

Discard

ExpectedReturnMiddle and High

ExpectedReturnLow and High

ExpectedReturnLow and Middle

A-K-Q

Q

1.423

1.309

1.263

A-K-J

J

1.429

1.186

1.155

A-K-10

10

1.431

1.092

1.074

A-K-9

9

1.443

0.943

0.924

A-K-8

8

1.438

0.888

0.814

A-K-7

7

1.441

0.846

0.781

A-K-6

6

1.440

0.814

0.756

A-K-5

5

1.443

0.856

0.733

A-K-4

4

1.440

0.835

0.712

A-K-3

3

1.431

0.809

0.690

A-K-2

2

1.420

0.773

0.669

A-Q-J

J

1.272

1.186

1.099

A-Q-10

10

1.273

1.091

1.028

A-Q-9

9

1.288

0.940

0.890

A-Q-8

8

1.285

0.889

0.783

A-Q-7

7

1.284

0.850

0.700

A-Q-6

6

1.286

0.813

0.682

A-Q-5

5

1.288

0.859

0.663

A-Q-4

4

1.284

0.834

0.642

A-Q-3

3

1.279

0.811

0.622

A-Q-2

2

1.271

0.777

0.607

A-J-10

10

1.154

1.091

1.017

A-J-9

9

1.169

0.941

0.890

A-J-8

8

1.169

0.888

0.785

A-J-7

7

1.169

0.850

0.697

A-J-6

6

1.169

0.819

0.626

A-J-5

5

1.172

0.861

0.611

A-J-4

4

1.170

0.838

0.591

A-J-3

3

1.164

0.812

0.572

A-J-2

2

1.156

0.778

0.558

A-10-9

9

1.080

0.941

0.905

A-10-8

8

1.080

0.888

0.809

A-10-7

7

1.079

0.848

0.721

A-10-6

6

1.082

0.818

0.643

A-10-5

5

1.086

0.866

0.576

A-10-4

4

1.083

0.838

0.558

A-10-3

3

1.078

0.811

0.542

A-10-2

2

1.072

0.778

0.528

A-9-8

8

0.915

0.880

0.805

A-9-7

7

0.916

0.842

0.741

A-9-6

6

0.917

0.811

0.666

A-9-5

5

0.921

0.860

0.592

A-9-4

4

0.919

0.837

0.521

A-9-3

3

0.916

0.809

0.508

A-9-2

2

0.910

0.774

0.494

A-8-7

7

0.862

0.838

0.757

A-8-6

6

0.864

0.809

0.705

A-8-5

5

0.870

0.858

0.632

A-8-4

4

0.868

0.834

0.553

A-8-3

3

0.866

0.815

0.487

A-8-2

2

0.863

0.775

0.479

A-7-6

6

0.827

0.805

0.729

A-7-5

7

0.830

0.855

0.677

A-7-4

7

0.829

0.832

0.603

A-7-3

3

0.828

0.811

0.523

A-7-2

2

0.827

0.782

0.463

A-6-5

6

0.798

0.857

0.710

A-6-4

6

0.796

0.835

0.652

A-6-3

6

0.795

0.811

0.581

A-6-2

2

0.796

0.781

0.505

A-5-4

4

0.830

0.814

0.680

A-5-3

3

0.827

0.791

0.624

A-5-2

2

0.827

0.762

0.554

A-4-3

3

0.804

0.789

0.591

A-4-2

2

0.803

0.760

0.537

A-3-2

2

0.782

0.758

0.508

K-Q-J

J

1.166

1.093

1.081

K-Q-10

10

1.165

1.013

1.011

K-Q-9

9

1.183

0.869

0.873

K-Q-8

8

1.195

0.782

0.787

K-Q-7

7

1.195

0.753

0.700

K-Q-6

6

1.194

0.727

0.683

K-Q-5

5

1.193

0.707

0.665

K-Q-4

4

1.190

0.685

0.644

K-Q-3

3

1.185

0.665

0.625

K-Q-2

2

1.180

0.647

0.610

K-J-10

10

1.065

1.013

1.002

K-J-9

9

1.082

0.870

0.872

K-J-8

8

1.096

0.783

0.789

K-J-7

7

1.095

0.752

0.695

K-J-6

6

1.094

0.731

0.625

K-J-5

5

1.095

0.707

0.611

K-J-4

4

1.093

0.686

0.592

K-J-3

3

1.089

0.666

0.575

K-J-2

2

1.083

0.646

0.559

K-10-9

9

1.009

0.868

0.890

K-10-8

8

1.023

0.780

0.813

K-10-7

7

1.021

0.751

0.721

K-10-6

6

1.023

0.730

0.642

K-10-5

5

1.023

0.712

0.576

K-10-4

4

1.023

0.688

0.560

K-10-3

3

1.018

0.666

0.544

K-10-2

2

1.013

0.646

0.530

K-9-8

8

0.857

0.778

0.810

K-9-7

7

0.856

0.747

0.740

K-9-6

6

0.859

0.726

0.666

K-9-5

5

0.860

0.709

0.593

K-9-4

4

0.857

0.687

0.523

K-9-3

3

0.856

0.664

0.511

K-9-2

2

0.851

0.645

0.499

K-8-7

K

0.761

0.743

0.767

K-8-6

6

0.761

0.723

0.710

K-8-5

5

0.764

0.704

0.637

K-8-4

4

0.762

0.683

0.558

K-8-3

3

0.761

0.665

0.493

K-8-2

2

0.759

0.643

0.483

K-7-6

6

0.732

0.721

0.731

K-7-5

5

0.732

0.703

0.680

K-7-4

4

0.734

0.682

0.605

K-7-3

3

0.733

0.664

0.528

K-7-2

2

0.731

0.647

0.465

K-6-5

K

0.708

0.698

0.712

K-6-4

4

0.708

0.679

0.653

K-6-3

3

0.709

0.663

0.581

K-6-2

2

0.711

0.646

0.506

K-5-4

K

0.690

0.676

0.701

K-5-3

3

0.689

0.657

0.643

K-5-2

2

0.689

0.641

0.572

K-4-3

3

0.668

0.656

0.610

K-4-2

2

0.667

0.639

0.555

K-3-2

2

0.649

0.637

0.526

Q-J-10

10

1.005

0.964

0.984

Q-J-9

9

1.024

0.829

0.855

Q-J-8

8

1.038

0.745

0.773

Q-J-7

7

1.054

0.678

0.701

Q-J-6

6

1.051

0.662

0.624

Q-J-5

5

1.054

0.643

0.610

Q-J-4

4

1.051

0.624

0.592

Q-J-3

3

1.046

0.605

0.574

Q-J-2

2

1.043

0.589

0.559

Q-10-9

9

0.961

0.827

0.872

Q-10-8

8

0.978

0.744

0.796

Q-10-7

7

0.993

0.677

0.726

Q-10-6

6

0.992

0.662

0.640

Q-10-5

5

0.993

0.647

0.574

Q-10-4

4

0.992

0.624

0.558

Q-10-3

3

0.989

0.607

0.544

Q-10-2

2

0.985

0.589

0.529

Q-9-8

8

0.819

0.740

0.795

Q-9-7

7

0.835

0.675

0.746

Q-9-6

6

0.836

0.660

0.667

Q-9-5

5

0.836

0.644

0.591

Q-9-4

4

0.835

0.626

0.522

Q-9-3

3

0.835

0.605

0.511

Q-9-2

2

0.831

0.590

0.497

Q-8-7

Q

0.740

0.671

0.770

Q-8-6

6

0.739

0.655

0.708

Q-8-5

5

0.739

0.640

0.636

Q-8-4

4

0.741

0.624

0.558

Q-8-3

3

0.740

0.607

0.492

Q-8-2

2

0.737

0.586

0.482

Q-7-6

Q

0.660

0.654

0.741

Q-7-5

Q

0.662

0.640

0.685

Q-7-4

4

0.662

0.620

0.608

Q-7-3

3

0.663

0.606

0.531

Q-7-2

2

0.662

0.590

0.469

Q-6-5

Q

0.644

0.636

0.712

Q-6-4

Q

0.646

0.618

0.654

Q-6-3

3

0.646

0.603

0.582

Q-6-2

2

0.647

0.588

0.507

Q-5-4

Q

0.628

0.616

0.700

Q-5-3

Q

0.628

0.598

0.645

Q-5-2

2

0.629

0.584

0.573

Q-4-3

Q

0.608

0.597

0.612

Q-4-2

2

0.608

0.582

0.556

Q-3-2

2

0.593

0.583

0.526

J-10-9

9

0.943

0.815

0.857

J-10-8

8

0.958

0.734

0.778

J-10-7

7

0.975

0.667

0.710

J-10-6

6

0.992

0.610

0.648

J-10-5

5

0.992

0.597

0.574

J-10-4

4

0.988

0.575

0.557

J-10-3

3

0.987

0.559

0.541

J-10-2

2

0.984

0.545

0.528

J-9-8

8

0.812

0.734

0.778

J-9-7

7

0.828

0.665

0.730

J-9-6

6

0.843

0.607

0.671

J-9-5

5

0.842

0.596

0.591

J-9-4

4

0.844

0.579

0.521

J-9-3

3

0.841

0.559

0.508

J-9-2

2

0.839

0.544

0.496

J-8-7

J

0.734

0.663

0.756

J-8-6

6

0.750

0.605

0.715

J-8-5

5

0.750

0.594

0.635

J-8-4

4

0.749

0.577

0.556

J-8-3

3

0.750

0.562

0.492

J-8-2

2

0.749

0.545

0.482

J-7-6

J

0.664

0.602

0.746

J-7-5

J

0.662

0.590

0.684

J-7-4

4

0.667

0.575

0.607

J-7-3

3

0.667

0.560

0.530

J-7-2

2

0.666

0.548

0.468

J-6-5

J

0.595

0.590

0.721

J-6-4

J

0.596

0.574

0.658

J-6-3

3

0.597

0.559

0.586

J-6-2

2

0.598

0.545

0.510

J-5-4

J

0.581

0.569

0.701

J-5-3

J

0.584

0.556

0.646

J-5-2

2

0.585

0.543

0.574

J-4-3

J

0.565

0.555

0.613

J-4-2

2

0.565

0.542

0.556

J-3-2

2

0.549

0.540

0.526

10-9-8

8

0.821

0.746

0.762

10-9-7

7

0.836

0.678

0.712

10-9-6

6

0.854

0.615

0.655

10-9-5

5

0.868

0.563

0.594

10-9-4

4

0.866

0.548

0.520

10-9-3

3

0.867

0.529

0.507

10-9-2

2

0.865

0.517

0.494

10-8-7

7

0.749

0.677

0.739

10-8-6

6

0.763

0.614

0.698

10-8-5

5

0.780

0.561

0.642

10-8-4

4

0.779

0.547

0.555

10-8-3

3

0.780

0.534

0.489

10-8-2

2

0.779

0.518

0.481

10-7-6

10

0.681

0.612

0.730

10-7-5

5

0.696

0.559

0.688

10-7-4

4

0.696

0.546

0.606

10-7-3

3

0.697

0.533

0.527

10-7-2

2

0.697

0.522

0.466

10-6-5

10

0.619

0.558

0.725

10-6-4

10

0.616

0.543

0.657

10-6-3

3

0.619

0.531

0.585

10-6-2

2

0.619

0.520

0.508

10-5-4

10

0.552

0.541

0.708

10-5-3

10

0.553

0.527

0.649

10-5-2

10

0.553

0.516

0.576

10-4-3

10

0.538

0.528

0.612

10-4-2

10

0.537

0.516

0.557

10-3-2

10

0.525

0.516

0.528

9-8-7

7

0.725

0.680

0.721

9-8-6

6

0.741

0.622

0.679

9-8-5

5

0.756

0.564

0.623

9-8-4

4

0.773

0.508

0.559

9-8-3

3

0.774

0.498

0.487

9-8-2

2

0.772

0.483

0.477

9-7-6

9

0.682

0.620

0.710

9-7-5

5

0.698

0.562

0.670

9-7-4

4

0.715

0.506

0.611

9-7-3

3

0.716

0.497

0.526

9-7-2

2

0.716

0.486

0.464

9-6-5

9

0.626

0.560

0.709

9-6-4

9

0.644

0.505

0.662

9-6-3

3

0.643

0.495

0.583

9-6-2

2

0.645

0.482

0.506

9-5-4

9

0.568

0.502

0.711

9-5-3

9

0.569

0.492

0.647

9-5-2

9

0.572

0.483

0.575

9-4-3

9

0.501

0.493

0.618

9-4-2

9

0.501

0.483

0.561

9-3-2

9

0.490

0.481

0.526

8-7-6

8

0.692

0.650

0.694

8-7-5

5

0.705

0.594

0.652

8-7-4

4

0.725

0.530

0.593

8-7-3

3

0.742

0.479

0.531

8-7-2

2

0.739

0.471

0.461

8-6-5

8

0.654

0.592

0.692

8-6-4

4

0.672

0.528

0.644

8-6-3

3

0.690

0.477

0.589

8-6-2

2

0.690

0.469

0.503

8-5-4

8

0.601

0.527

0.695

8-5-3

8

0.618

0.476

0.652

8-5-2

2

0.618

0.468

0.572

8-4-3

8

0.540

0.476

0.623

8-4-2

8

0.539

0.470

0.559

8-3-2

8

0.474

0.469

0.534

7-6-5

7

0.667

0.625

0.674

7-6-4

4

0.685

0.565

0.627

7-6-3

3

0.704

0.504

0.571

7-6-2

2

0.719

0.455

0.510

7-5-4

7

0.632

0.562

0.678

7-5-3

3

0.650

0.501

0.635

7-5-2

2

0.668

0.452

0.579

7-4-3

7

0.576

0.502

0.607

7-4-2

2

0.592

0.454

0.563

7-3-2

7

0.517

0.456

0.539

6-5-4

6

0.651

0.598

0.662

6-5-3

3

0.669

0.541

0.616

6-5-2

2

0.685

0.482

0.561

6-4-3

3

0.611

0.543

0.588

6-4-2

2

0.629

0.483

0.546

6-3-2

2

0.558

0.486

0.522

5-4-3

3

0.640

0.588

0.566

5-4-2

2

0.658

0.533

0.521

5-3-2

2

0.602

0.535

0.498

4-3-2

2

0.572

0.519

0.500

Three Singletons — Lowest Two Suited

The following table shows the expected return for all three possible plays when dealt three singletons when the lowest two are suited. 60.5% of the time, the best play is to keep the suited cards and discard the highest. The rest of the time, discard the lowest card. The following table shows the expected return for all three ways ways to choose two of the three cards.

Three Singletons — Lowest Two Suited

Hand

Discard

ExpectedReturnMiddle and High

ExpectedReturnLow and High

ExpectedReturnLow and Middle

A-K-Q

A

1.404

1.296

1.480

A-K-J

J

1.407

1.175

1.379

A-K-10

10

1.408

1.082

1.304

A-K-9

9

1.421

0.936

1.168

A-K-8

8

1.419

0.884

1.068

A-K-7

7

1.419

0.840

1.037

A-K-6

6

1.419

0.808

1.015

A-K-5

5

1.421

0.853

0.995

A-K-4

4

1.416

0.829

0.976

A-K-3

3

1.409

0.805

0.953

A-K-2

2

1.396

0.770

0.934

A-Q-J

A

1.255

1.175

1.317

A-Q-10

10

1.257

1.081

1.255

A-Q-9

9

1.269

0.933

1.129

A-Q-8

8

1.268

0.884

1.030

A-Q-7

7

1.268

0.845

0.953

A-Q-6

6

1.269

0.809

0.939

A-Q-5

5

1.271

0.856

0.923

A-Q-4

4

1.269

0.833

0.904

A-Q-3

3

1.262

0.809

0.886

A-Q-2

2

1.252

0.773

0.868

A-J-10

A

1.140

1.082

1.238

A-J-9

9

1.156

0.936

1.122

A-J-8

8

1.155

0.883

1.024

A-J-7

7

1.157

0.845

0.945

A-J-6

6

1.154

0.814

0.879

A-J-5

5

1.160

0.857

0.866

A-J-4

4

1.156

0.833

0.848

A-J-3

3

1.150

0.809

0.831

A-J-2

2

1.143

0.775

0.818

A-10-9

A

1.068

0.935

1.131

A-10-8

8

1.070

0.881

1.041

A-10-7

7

1.067

0.843

0.962

A-10-6

6

1.069

0.812

0.888

A-10-5

5

1.074

0.861

0.824

A-10-4

4

1.071

0.834

0.811

A-10-3

3

1.068

0.809

0.796

A-10-2

2

1.061

0.775

0.782

A-9-8

A

0.904

0.875

1.034

A-9-7

A

0.906

0.836

0.975

A-9-6

6

0.908

0.807

0.905

A-9-5

5

0.912

0.856

0.838

A-9-4

4

0.911

0.834

0.773

A-9-3

3

0.906

0.805

0.760

A-9-2

2

0.902

0.772

0.751

A-8-7

A

0.855

0.835

0.987

A-8-6

A

0.856

0.805

0.939

A-8-5

A

0.862

0.853

0.873

A-8-4

4

0.862

0.832

0.799

A-8-3

3

0.857

0.810

0.734

A-8-2

2

0.854

0.772

0.726

A-7-6

A

0.820

0.802

0.958

A-7-5

A

0.821

0.849

0.908

A-7-4

A

0.821

0.828

0.839

A-7-3

3

0.821

0.807

0.764

A-7-2

2

0.819

0.778

0.705

A-6-5

A

0.791

0.853

0.937

A-6-4

A

0.789

0.827

0.880

A-6-3

A

0.789

0.807

0.814

A-6-2

2

0.790

0.779

0.742

A-5-4

A

0.824

0.810

0.906

A-5-3

A

0.822

0.787

0.849

A-5-2

2

0.823

0.760

0.784

A-4-3

A

0.799

0.786

0.818

A-4-2

2

0.801

0.758

0.764

A-3-2

2

0.778

0.753

0.735

K-Q-J

K

1.148

1.082

1.300

K-Q-10

K

1.148

1.005

1.238

K-Q-9

9

1.164

0.862

1.114

K-Q-8

8

1.177

0.776

1.032

K-Q-7

7

1.175

0.748

0.953

K-Q-6

6

1.178

0.723

0.938

K-Q-5

5

1.177

0.705

0.923

K-Q-4

4

1.171

0.680

0.906

K-Q-3

3

1.171

0.664

0.885

K-Q-2

2

1.161

0.642

0.870

K-J-10

K

1.054

1.005

1.223

K-J-9

K

1.069

0.861

1.105

K-J-8

8

1.081

0.776

1.031

K-J-7

7

1.084

0.749

0.944

K-J-6

6

1.080

0.726

0.879

K-J-5

5

1.083

0.705

0.867

K-J-4

4

1.079

0.682

0.849

K-J-3

3

1.077

0.663

0.833

K-J-2

2

1.068

0.643

0.819

K-10-9

K

0.996

0.861

1.116

K-10-8

K

1.011

0.774

1.044

K-10-7

7

1.011

0.748

0.960

K-10-6

6

1.014

0.727

0.889

K-10-5

5

1.011

0.707

0.828

K-10-4

4

1.011

0.684

0.814

K-10-3

3

1.007

0.663

0.798

K-10-2

2

1.001

0.643

0.783

K-9-8

K

0.846

0.769

1.038

K-9-7

K

0.849

0.744

0.976

K-9-6

K

0.849

0.722

0.907

K-9-5

5

0.851

0.705

0.840

K-9-4

4

0.848

0.683

0.775

K-9-3

3

0.848

0.663

0.763

K-9-2

2

0.844

0.643

0.751

K-8-7

K

0.751

0.737

0.994

K-8-6

K

0.752

0.716

0.943

K-8-5

K

0.756

0.698

0.877

K-8-4

K

0.757

0.682

0.803

K-8-3

3

0.753

0.662

0.741

K-8-2

2

0.749

0.639

0.732

K-7-6

K

0.725

0.717

0.961

K-7-5

K

0.727

0.699

0.911

K-7-4

K

0.727

0.680

0.840

K-7-3

K

0.728

0.662

0.768

K-7-2

2

0.727

0.645

0.709

K-6-5

K

0.704

0.695

0.940

K-6-4

K

0.703

0.676

0.883

K-6-3

K

0.703

0.659

0.815

K-6-2

K

0.703

0.641

0.745

K-5-4

K

0.683

0.671

0.925

K-5-3

K

0.684

0.653

0.868

K-5-2

K

0.683

0.636

0.801

K-4-3

K

0.664

0.651

0.837

K-4-2

K

0.663

0.635

0.782

K-3-2

K

0.645

0.633

0.750

Q-J-10

Q

0.994

0.956

1.205

Q-J-9

Q

1.011

0.822

1.089

Q-J-8

8

1.026

0.738

1.013

Q-J-7

7

1.041

0.674

0.948

Q-J-6

6

1.041

0.658

0.877

Q-J-5

5

1.041

0.641

0.866

Q-J-4

4

1.039

0.621

0.850

Q-J-3

3

1.034

0.601

0.834

Q-J-2

2

1.030

0.585

0.818

Q-10-9

Q

0.953

0.822

1.101

Q-10-8

Q

0.965

0.737

1.029

Q-10-7

7

0.982

0.672

0.964

Q-10-6

6

0.981

0.658

0.886

Q-10-5

5

0.982

0.645

0.825

Q-10-4

4

0.980

0.619

0.813

Q-10-3

3

0.977

0.603

0.796

Q-10-2

2

0.974

0.586

0.781

Q-9-8

Q

0.812

0.737

1.027

Q-9-7

Q

0.826

0.669

0.980

Q-9-6

Q

0.826

0.655

0.906

Q-9-5

Q

0.827

0.640

0.838

Q-9-4

4

0.828

0.622

0.774

Q-9-3

3

0.827

0.603

0.763

Q-9-2

2

0.823

0.587

0.750

Q-8-7

Q

0.729

0.665

0.999

Q-8-6

Q

0.732

0.651

0.943

Q-8-5

Q

0.732

0.637

0.873

Q-8-4

Q

0.733

0.620

0.803

Q-8-3

Q

0.734

0.605

0.741

Q-8-2

Q

0.730

0.586

0.731

Q-7-6

Q

0.651

0.647

0.968

Q-7-5

Q

0.652

0.633

0.917

Q-7-4

Q

0.656

0.618

0.846

Q-7-3

Q

0.657

0.600

0.772

Q-7-2

Q

0.655

0.587

0.713

Q-6-5

Q

0.639

0.633

0.938

Q-6-4

Q

0.638

0.615

0.882

Q-6-3

Q

0.640

0.599

0.816

Q-6-2

Q

0.641

0.585

0.747

Q-5-4

Q

0.624

0.612

0.927

Q-5-3

Q

0.622

0.595

0.870

Q-5-2

Q

0.624

0.582

0.804

Q-4-3

Q

0.605

0.594

0.838

Q-4-2

Q

0.605

0.580

0.783

Q-3-2

Q

0.590

0.579

0.751

J-10-9

J

0.930

0.808

1.084

J-10-8

J

0.946

0.729

1.014

J-10-7

7

0.964

0.660

0.951

J-10-6

6

0.981

0.606

0.893

J-10-5

5

0.979

0.594

0.827

J-10-4

4

0.979

0.572

0.811

J-10-3

3

0.975

0.554

0.795

J-10-2

2

0.972

0.541

0.782

J-9-8

J

0.803

0.729

1.012

J-9-7

J

0.818

0.658

0.966

J-9-6

J

0.834

0.603

0.911

J-9-5

J

0.833

0.592

0.838

J-9-4

4

0.835

0.575

0.773

J-9-3

3

0.833

0.556

0.760

J-9-2

2

0.831

0.541

0.748

J-8-7

J

0.727

0.657

0.986

J-8-6

J

0.743

0.602

0.948

J-8-5

J

0.743

0.591

0.875

J-8-4

J

0.743

0.575

0.803

J-8-3

3

0.742

0.558

0.738

J-8-2

2

0.743

0.544

0.731

J-7-6

J

0.660

0.600

0.972

J-7-5

J

0.657

0.587

0.916

J-7-4

J

0.659

0.571

0.843

J-7-3

J

0.660

0.558

0.770

J-7-2

J

0.660

0.545

0.711

J-6-5

J

0.588

0.584

0.946

J-6-4

J

0.590

0.569

0.887

J-6-3

J

0.592

0.554

0.817

J-6-2

J

0.594

0.542

0.747

J-5-4

J

0.577

0.567

0.924

J-5-3

J

0.579

0.553

0.871

J-5-2

J

0.579

0.540

0.803

J-4-3

J

0.561

0.551

0.838

J-4-2

J

0.562

0.540

0.783

J-3-2

J

0.545

0.538

0.752

10-9-8

10

0.812

0.739

0.994

10-9-7

10

0.826

0.671

0.948

10-9-6

10

0.843

0.611

0.894

10-9-5

5

0.861

0.559

0.842

10-9-4

4

0.859

0.544

0.770

10-9-3

3

0.859

0.528

0.757

10-9-2

2

0.857

0.513

0.748

10-8-7

10

0.740

0.671

0.969

10-8-6

10

0.756

0.610

0.934

10-8-5

10

0.772

0.557

0.879

10-8-4

10

0.772

0.543

0.798

10-8-3

3

0.773

0.531

0.737

10-8-2

2

0.772

0.515

0.729

10-7-6

10

0.675

0.608

0.959

10-7-5

10

0.689

0.555

0.920

10-7-4

10

0.690

0.543

0.844

10-7-3

10

0.692

0.529

0.767

10-7-2

10

0.690

0.517

0.709

10-6-5

10

0.612

0.554

0.952

10-6-4

10

0.611

0.540

0.884

10-6-3

10

0.615

0.528

0.818

10-6-2

10

0.616

0.517

0.747

10-5-4

10

0.546

0.538

0.932

10-5-3

10

0.548

0.525

0.873

10-5-2

10

0.549

0.515

0.804

10-4-3

10

0.533

0.524

0.837

10-4-2

10

0.533

0.513

0.785

10-3-2

10

0.521

0.513

0.753

9-8-7

9

0.719

0.674

0.952

9-8-6

9

0.731

0.617

0.914

9-8-5

9

0.751

0.559

0.863

9-8-4

9

0.768

0.504

0.805

9-8-3

3

0.765

0.495

0.734

9-8-2

2

0.763

0.480

0.726

9-7-6

9

0.674

0.614

0.941

9-7-5

9

0.691

0.558

0.904

9-7-4

9

0.711

0.503

0.847

9-7-3

9

0.711

0.493

0.765

9-7-2

2

0.709

0.484

0.708

9-6-5

9

0.620

0.557

0.935

9-6-4

9

0.636

0.501

0.891

9-6-3

9

0.639

0.491

0.814

9-6-2

9

0.639

0.480

0.743

9-5-4

9

0.563

0.497

0.934

9-5-3

9

0.563

0.489

0.872

9-5-2

9

0.566

0.480

0.802

9-4-3

9

0.494

0.488

0.843

9-4-2

9

0.497

0.479

0.788

9-3-2

9

0.487

0.480

0.753

8-7-6

8

0.685

0.645

0.924

8-7-5

8

0.699

0.590

0.888

8-7-4

8

0.717

0.526

0.829

8-7-3

8

0.735

0.476

0.771

8-7-2

2

0.733

0.468

0.708

8-6-5

8

0.648

0.585

0.919

8-6-4

8

0.667

0.526

0.874

8-6-3

8

0.684

0.473

0.820

8-6-2

8

0.684

0.467

0.741

8-5-4

8

0.594

0.523

0.922

8-5-3

8

0.615

0.471

0.877

8-5-2

8

0.613

0.466

0.800

8-4-3

8

0.535

0.471

0.846

8-4-2

8

0.535

0.467

0.783

8-3-2

8

0.470

0.467

0.761

7-6-5

7

0.662

0.622

0.903

7-6-4

7

0.679

0.560

0.856

7-6-3

7

0.696

0.500

0.804

7-6-2

7

0.713

0.452

0.745

7-5-4

7

0.627

0.559

0.905

7-5-3

7

0.646

0.498

0.860

7-5-2

7

0.663

0.450

0.807

7-4-3

7

0.570

0.498

0.833

7-4-2

7

0.591

0.453

0.790

7-3-2

7

0.512

0.452

0.765

6-5-4

6

0.646

0.594

0.884

6-5-3

6

0.664

0.538

0.844

6-5-2

6

0.681

0.480

0.787

6-4-3

6

0.605

0.538

0.814

6-4-2

6

0.625

0.481

0.771

6-3-2

6

0.556

0.483

0.747

5-4-3

5

0.638

0.584

0.793

5-4-2

5

0.654

0.529

0.752

5-3-2

5

0.599

0.532

0.728

4-3-2

4

0.566

0.517

0.726

Three Singletons — Outside Two Suited

The following table shows the expected return for all three possible plays when dealt three singletons when the lowest and highest two are suited. 74.1% of the time, the best play is to keep the suited cards and discard the middle. The following table shows the expected return for all three ways ways to choose two of the three cards.

Three Singletons — Outside Two Suited

Hand

Discard

ExpectedReturnMiddle and High

ExpectedReturnLow and High

ExpectedReturnLow and Middle

A-K-Q

K

1.400

1.533

1.256

A-K-J

K

1.405

1.417

1.146

A-K-10

10

1.404

1.332

1.065

A-K-9

9

1.419

1.196

0.918

A-K-8

8

1.415

1.147

0.810

A-K-7

7

1.418

1.109

0.778

A-K-6

6

1.416

1.080

0.749

A-K-5

5

1.417

1.119

0.729

A-K-4

4

1.413

1.098

0.706

A-K-3

3

1.405

1.078

0.686

A-K-2

2

1.397

1.045

0.666

A-Q-J

Q

1.244

1.416

1.088

A-Q-10

Q

1.250

1.329

1.021

A-Q-9

9

1.263

1.194

0.885

A-Q-8

8

1.260

1.144

0.778

A-Q-7

7

1.260

1.111

0.696

A-Q-6

6

1.260

1.078

0.678

A-Q-5

5

1.263

1.124

0.660

A-Q-4

4

1.260

1.103

0.641

A-Q-3

3

1.253

1.081

0.620

A-Q-2

2

1.248

1.048

0.605

A-J-10

J

1.133

1.331

1.011

A-J-9

J

1.147

1.195

0.884

A-J-8

J

1.145

1.147

0.780

A-J-7

7

1.144

1.112

0.694

A-J-6

6

1.144

1.084

0.623

A-J-5

5

1.146

1.125

0.606

A-J-4

4

1.144

1.103

0.587

A-J-3

3

1.139

1.082

0.572

A-J-2

2

1.134

1.050

0.557

A-10-9

10

1.055

1.194

0.899

A-10-8

10

1.057

1.149

0.802

A-10-7

10

1.054

1.109

0.718

A-10-6

10

1.059

1.083

0.641

A-10-5

10

1.063

1.131

0.572

A-10-4

10

1.057

1.102

0.554

A-10-3

10

1.055

1.081

0.541

A-10-2

10

1.048

1.049

0.525

A-9-8

9

0.891

1.138

0.799

A-9-7

9

0.892

1.103

0.737

A-9-6

9

0.894

1.076

0.663

A-9-5

9

0.900

1.124

0.590

A-9-4

9

0.895

1.104

0.518

A-9-3

9

0.891

1.075

0.504

A-9-2

9

0.890

1.046

0.495

A-8-7

8

0.839

1.102

0.751

A-8-6

8

0.842

1.075

0.702

A-8-5

8

0.843

1.119

0.630

A-8-4

8

0.844

1.101

0.550

A-8-3

8

0.844

1.083

0.485

A-8-2

8

0.839

1.048

0.475

A-7-6

7

0.802

1.070

0.726

A-7-5

7

0.805

1.117

0.673

A-7-4

7

0.807

1.099

0.600

A-7-3

7

0.806

1.081

0.520

A-7-2

7

0.805

1.054

0.461

A-6-5

6

0.775

1.120

0.707

A-6-4

6

0.774

1.102

0.649

A-6-3

6

0.773

1.080

0.578

A-6-2

6

0.773

1.055

0.502

A-5-4

5

0.805

1.078

0.678

A-5-3

5

0.807

1.061

0.622

A-5-2

5

0.805

1.034

0.553

A-4-3

4

0.782

1.059

0.588

A-4-2

4

0.782

1.033

0.533

A-3-2

3

0.760

1.030

0.504

K-Q-J

Q

1.144

1.318

1.073

K-Q-10

Q

1.147

1.249

1.006

K-Q-9

9

1.162

1.116

0.867

K-Q-8

8

1.175

1.038

0.783

K-Q-7

7

1.171

1.009

0.694

K-Q-6

6

1.173

0.985

0.679

K-Q-5

5

1.172

0.969

0.661

K-Q-4

4

1.172

0.951

0.643

K-Q-3

3

1.166

0.935

0.623

K-Q-2

2

1.159

0.914

0.607

K-J-10

J

1.047

1.246

0.994

K-J-9

J

1.063

1.115

0.865

K-J-8

8

1.078

1.037

0.783

K-J-7

7

1.075

1.008

0.691

K-J-6

6

1.076

0.991

0.622

K-J-5

5

1.078

0.973

0.608

K-J-4

4

1.073

0.952

0.589

K-J-3

3

1.069

0.935

0.571

K-J-2

2

1.061

0.914

0.556

K-10-9

10

0.988

1.112

0.882

K-10-8

10

1.002

1.035

0.808

K-10-7

10

1.003

1.008

0.715

K-10-6

6

1.005

0.991

0.638

K-10-5

5

1.005

0.977

0.574

K-10-4

4

1.003

0.952

0.557

K-10-3

3

0.998

0.934

0.541

K-10-2

2

0.994

0.917

0.527

K-9-8

9

0.838

1.032

0.805

K-9-7

9

0.838

1.005

0.737

K-9-6

9

0.841

0.986

0.664

K-9-5

9

0.842

0.974

0.591

K-9-4

9

0.841

0.954

0.522

K-9-3

9

0.838

0.933

0.508

K-9-2

9

0.831

0.913

0.496

K-8-7

8

0.743

1.001

0.763

K-8-6

8

0.742

0.981

0.705

K-8-5

8

0.744

0.968

0.635

K-8-4

8

0.745

0.949

0.556

K-8-3

8

0.745

0.937

0.491

K-8-2

8

0.741

0.912

0.481

K-7-6

7

0.714

0.983

0.729

K-7-5

7

0.714

0.964

0.677

K-7-4

7

0.715

0.950

0.603

K-7-3

7

0.716

0.933

0.526

K-7-2

7

0.714

0.917

0.463

K-6-5

6

0.690

0.964

0.709

K-6-4

6

0.692

0.947

0.650

K-6-3

6

0.692

0.928

0.580

K-6-2

6

0.693

0.913

0.505

K-5-4

5

0.670

0.942

0.695

K-5-3

5

0.672

0.927

0.641

K-5-2

5

0.672

0.909

0.570

K-4-3

4

0.653

0.926

0.609

K-4-2

4

0.652

0.908

0.553

K-3-2

3

0.632

0.906

0.524

Q-J-10

J

0.991

1.193

0.974

Q-J-9

J

1.009

1.069

0.849

Q-J-8

8

1.023

0.993

0.766

Q-J-7

7

1.038

0.933

0.697

Q-J-6

6

1.037

0.920

0.622

Q-J-5

5

1.037

0.902

0.607

Q-J-4

4

1.036

0.885

0.589

Q-J-3

3

1.035

0.872

0.572

Q-J-2

2

1.026

0.851

0.555

Q-10-9

10

0.945

1.067

0.865

Q-10-8

10

0.965

0.991

0.792

Q-10-7

7

0.978

0.933

0.721

Q-10-6

6

0.976

0.920

0.637

Q-10-5

5

0.977

0.904

0.572

Q-10-4

4

0.976

0.884

0.554

Q-10-3

3

0.975

0.868

0.540

Q-10-2

2

0.971

0.854

0.527

Q-9-8

9

0.807

0.989

0.790

Q-9-7

9

0.821

0.929

0.742

Q-9-6

9

0.820

0.915

0.662

Q-9-5

9

0.820

0.903

0.587

Q-9-4

9

0.821

0.888

0.518

Q-9-3

9

0.824

0.870

0.509

Q-9-2

9

0.817

0.852

0.494

Q-8-7

8

0.723

0.925

0.766

Q-8-6

8

0.724

0.912

0.704

Q-8-5

8

0.724

0.901

0.633

Q-8-4

8

0.726

0.884

0.555

Q-8-3

8

0.726

0.869

0.490

Q-8-2

8

0.725

0.853

0.482

Q-7-6

7

0.645

0.910

0.736

Q-7-5

7

0.646

0.897

0.681

Q-7-4

7

0.647

0.884

0.604

Q-7-3

7

0.649

0.868

0.528

Q-7-2

7

0.647

0.854

0.465

Q-6-5

6

0.630

0.898

0.710

Q-6-4

6

0.629

0.880

0.650

Q-6-3

6

0.631

0.865

0.581

Q-6-2

6

0.634

0.853

0.505

Q-5-4

5

0.613

0.877

0.697

Q-5-3

5

0.613

0.863

0.642

Q-5-2

5

0.614

0.850

0.571

Q-4-3

4

0.596

0.863

0.610

Q-4-2

4

0.595

0.848

0.554

Q-3-2

3

0.580

0.847

0.525

J-10-9

10

0.930

1.051

0.850

J-10-8

10

0.946

0.977

0.774

J-10-7

7

0.964

0.915

0.707

J-10-6

6

0.979

0.863

0.643

J-10-5

5

0.980

0.853

0.571

J-10-4

4

0.978

0.834

0.555

J-10-3

3

0.975

0.817

0.539

J-10-2

2

0.972

0.804

0.526

J-9-8

9

0.797

0.976

0.772

J-9-7

9

0.814

0.913

0.725

J-9-6

9

0.831

0.863

0.669

J-9-5

9

0.831

0.851

0.587

J-9-4

9

0.832

0.835

0.518

J-9-3

3

0.828

0.819

0.505

J-9-2

2

0.827

0.804

0.493

J-8-7

8

0.721

0.910

0.750

J-8-6

8

0.738

0.860

0.713

J-8-5

8

0.737

0.847

0.633

J-8-4

8

0.739

0.836

0.554

J-8-3

8

0.740

0.819

0.488

J-8-2

8

0.739

0.808

0.479

J-7-6

7

0.653

0.858

0.742

J-7-5

7

0.652

0.847

0.680

J-7-4

7

0.653

0.833

0.604

J-7-3

7

0.655

0.819

0.528

J-7-2

7

0.654

0.808

0.466

J-6-5

6

0.583

0.845

0.716

J-6-4

6

0.585

0.830

0.656

J-6-3

6

0.587

0.819

0.584

J-6-2

6

0.586

0.807

0.507

J-5-4

5

0.571

0.829

0.698

J-5-3

5

0.572

0.816

0.641

J-5-2

5

0.573

0.803

0.571

J-4-3

4

0.553

0.815

0.609

J-4-2

4

0.554

0.803

0.554

J-3-2

3

0.538

0.801

0.524

10-9-8

9

0.810

0.981

0.756

10-9-7

9

0.824

0.916

0.706

10-9-6

9

0.842

0.861

0.649

10-9-5

5

0.859

0.815

0.592

10-9-4

4

0.856

0.802

0.515

10-9-3

3

0.858

0.785

0.504

10-9-2

2

0.854

0.773

0.491

10-8-7

8

0.737

0.918

0.732

10-8-6

8

0.752

0.860

0.694

10-8-5

8

0.770

0.815

0.639

10-8-4

8

0.769

0.801

0.553

10-8-3

8

0.770

0.788

0.485

10-8-2

8

0.769

0.773

0.477

10-7-6

7

0.670

0.859

0.727

10-7-5

7

0.686

0.811

0.683

10-7-4

7

0.687

0.800

0.602

10-7-3

7

0.688

0.790

0.525

10-7-2

7

0.688

0.777

0.465

10-6-5

6

0.609

0.813

0.722

10-6-4

6

0.608

0.801

0.653

10-6-3

6

0.609

0.787

0.581

10-6-2

6

0.611

0.776

0.508

10-5-4

5

0.541

0.795

0.705

10-5-3

5

0.543

0.783

0.645

10-5-2

5

0.545

0.773

0.575

10-4-3

4

0.528

0.783

0.609

10-4-2

4

0.530

0.773

0.555

10-3-2

3

0.516

0.774

0.525

9-8-7

8

0.717

0.918

0.715

9-8-6

8

0.732

0.864

0.674

9-8-5

8

0.748

0.810

0.619

9-8-4

4

0.765

0.759

0.556

9-8-3

3

0.763

0.751

0.484

9-8-2

2

0.764

0.736

0.476

9-7-6

7

0.674

0.862

0.707

9-7-5

7

0.690

0.808

0.666

9-7-4

7

0.707

0.759

0.607

9-7-3

7

0.708

0.749

0.523

9-7-2

7

0.706

0.737

0.462

9-6-5

6

0.618

0.808

0.706

9-6-4

6

0.635

0.756

0.657

9-6-3

6

0.636

0.748

0.578

9-6-2

6

0.637

0.738

0.504

9-5-4

5

0.562

0.756

0.710

9-5-3

5

0.560

0.749

0.642

9-5-2

5

0.562

0.735

0.572

9-4-3

4

0.491

0.746

0.616

9-4-2

4

0.494

0.738

0.557

9-3-2

3

0.482

0.738

0.524

8-7-6

7

0.685

0.886

0.688

8-7-5

7

0.700

0.835

0.648

8-7-4

7

0.717

0.777

0.588

8-7-3

3

0.736

0.728

0.530

8-7-2

2

0.735

0.722

0.463

8-6-5

6

0.649

0.834

0.687

8-6-4

6

0.666

0.775

0.640

8-6-3

6

0.682

0.725

0.584

8-6-2

6

0.682

0.719

0.501

8-5-4

5

0.593

0.772

0.692

8-5-3

5

0.611

0.724

0.648

8-5-2

5

0.612

0.717

0.570

8-4-3

4

0.534

0.727

0.619

8-4-2

4

0.532

0.719

0.557

8-3-2

3

0.468

0.719

0.531

7-6-5

6

0.662

0.860

0.669

7-6-4

6

0.679

0.803

0.621

7-6-3

6

0.698

0.745

0.567

7-6-2

2

0.712

0.700

0.505

7-5-4

5

0.626

0.800

0.675

7-5-3

5

0.646

0.742

0.631

7-5-2

5

0.663

0.697

0.576

7-4-3

4

0.571

0.746

0.603

7-4-2

4

0.589

0.699

0.561

7-3-2

3

0.510

0.701

0.536

6-5-4

5

0.645

0.829

0.656

6-5-3

5

0.662

0.776

0.612

6-5-2

5

0.681

0.721

0.557

6-4-3

4

0.605

0.778

0.587

6-4-2

4

0.623

0.722

0.543

6-3-2

3

0.553

0.723

0.518

5-4-3

4

0.635

0.816

0.562

5-4-2

4

0.654

0.762

0.519

5-3-2

3

0.597

0.764

0.495

4-3-2

3

0.567

0.748

0.494

Three Singletons — Highest Two Suited

The following table shows the expected return for all three possible plays when dealt three singletons when the lowest two are suited. 100% of the time, the best play is to keep the suited cards and discard the lowest. The rest of the time, discard the lowest card. The following table shows the expected return for all three ways ways to choose two of the three cards.

Three Singletons — Highest Two Suited

Hand

Discard

ExpectedReturnMiddle and High

ExpectedReturnLow and High

ExpectedReturnLow and Middle

A-K-Q

Q

1.632

1.286

1.252

A-K-J

J

1.638

1.162

1.143

A-K-10

10

1.638

1.066

1.060

A-K-9

9

1.651

0.920

0.912

A-K-8

8

1.646

0.865

0.803

A-K-7

7

1.651

0.823

0.769

A-K-6

6

1.645

0.789

0.743

A-K-5

5

1.652

0.837

0.720

A-K-4

4

1.646

0.810

0.699

A-K-3

3

1.636

0.784

0.678

A-K-2

2

1.629

0.752

0.657

A-Q-J

J

1.493

1.160

1.088

A-Q-10

10

1.498

1.067

1.019

A-Q-9

9

1.512

0.921

0.881

A-Q-8

8

1.506

0.865

0.773

A-Q-7

7

1.506

0.827

0.691

A-Q-6

6

1.506

0.791

0.674

A-Q-5

5

1.510

0.837

0.654

A-Q-4

4

1.507

0.812

0.633

A-Q-3

3

1.499

0.786

0.613

A-Q-2

2

1.491

0.753

0.597

A-J-10

10

1.387

1.066

1.009

A-J-9

9

1.402

0.919

0.882

A-J-8

8

1.400

0.864

0.777

A-J-7

7

1.401

0.827

0.689

A-J-6

6

1.399

0.796

0.617

A-J-5

5

1.404

0.839

0.603

A-J-4

4

1.401

0.813

0.585

A-J-3

3

1.395

0.790

0.567

A-J-2

2

1.388

0.754

0.550

A-10-9

9

1.321

0.920

0.900

A-10-8

8

1.321

0.865

0.799

A-10-7

7

1.320

0.826

0.716

A-10-6

6

1.322

0.795

0.635

A-10-5

5

1.326

0.842

0.570

A-10-4

4

1.324

0.816

0.552

A-10-3

3

1.318

0.791

0.536

A-10-2

2

1.315

0.757

0.523

A-9-8

8

1.168

0.856

0.799

A-9-7

7

1.171

0.819

0.736

A-9-6

6

1.170

0.787

0.660

A-9-5

5

1.174

0.835

0.584

A-9-4

4

1.174

0.815

0.517

A-9-3

3

1.170

0.786

0.505

A-9-2

2

1.164

0.752

0.489

A-8-7

7

1.123

0.816

0.753

A-8-6

6

1.122

0.786

0.700

A-8-5

5

1.126

0.835

0.628

A-8-4

4

1.127

0.812

0.549

A-8-3

3

1.123

0.791

0.483

A-8-2

2

1.118

0.752

0.474

A-7-6

6

1.087

0.783

0.726

A-7-5

5

1.091

0.831

0.672

A-7-4

4

1.091

0.809

0.599

A-7-3

3

1.090

0.788

0.520

A-7-2

2

1.088

0.758

0.458

A-6-5

5

1.063

0.834

0.707

A-6-4

4

1.064

0.812

0.649

A-6-3

3

1.063

0.789

0.576

A-6-2

2

1.062

0.761

0.502

A-5-4

4

1.090

0.789

0.677

A-5-3

3

1.094

0.771

0.622

A-5-2

2

1.091

0.738

0.552

A-4-3

3

1.072

0.768

0.589

A-4-2

2

1.069

0.735

0.532

A-3-2

2

1.050

0.736

0.504

K-Q-J

J

1.384

1.072

1.071

K-Q-10

10

1.387

0.995

1.002

K-Q-9

9

1.398

0.849

0.862

K-Q-8

8

1.414

0.764

0.779

K-Q-7

7

1.412

0.733

0.689

K-Q-6

6

1.414

0.709

0.672

K-Q-5

5

1.411

0.689

0.655

K-Q-4

4

1.408

0.668

0.635

K-Q-3

3

1.402

0.647

0.617

K-Q-2

2

1.393

0.625

0.599

K-J-10

10

1.291

0.992

0.991

K-J-9

9

1.311

0.849

0.864

K-J-8

8

1.323

0.765

0.783

K-J-7

7

1.323

0.735

0.688

K-J-6

6

1.321

0.712

0.619

K-J-5

5

1.322

0.689

0.604

K-J-4

4

1.322

0.669

0.587

K-J-3

3

1.316

0.649

0.569

K-J-2

2

1.309

0.629

0.552

K-10-9

9

1.242

0.850

0.885

K-10-8

8

1.258

0.762

0.806

K-10-7

7

1.258

0.734

0.714

K-10-6

6

1.258

0.713

0.637

K-10-5

5

1.254

0.691

0.570

K-10-4

4

1.254

0.670

0.553

K-10-3

3

1.252

0.649

0.538

K-10-2

2

1.246

0.629

0.522

K-9-8

8

1.104

0.758

0.805

K-9-7

7

1.104

0.730

0.736

K-9-6

6

1.106

0.707

0.662

K-9-5

5

1.107

0.688

0.586

K-9-4

4

1.105

0.670

0.519

K-9-3

3

1.103

0.647

0.504

K-9-2

2

1.097

0.627

0.494

K-8-7

7

1.016

0.726

0.762

K-8-6

6

1.016

0.701

0.706

K-8-5

5

1.019

0.686

0.633

K-8-4

4

1.019

0.666

0.555

K-8-3

3

1.017

0.647

0.488

K-8-2

2

1.013

0.624

0.478

K-7-6

6

0.992

0.702

0.727

K-7-5

5

0.993

0.685

0.679

K-7-4

4

0.992

0.664

0.601

K-7-3

3

0.993

0.647

0.524

K-7-2

2

0.992

0.631

0.464

K-6-5

5

0.970

0.681

0.710

K-6-4

4

0.970

0.662

0.649

K-6-3

3

0.970

0.643

0.577

K-6-2

2

0.972

0.627

0.503

K-5-4

4

0.954

0.658

0.697

K-5-3

3

0.951

0.641

0.642

K-5-2

2

0.953

0.623

0.571

K-4-3

3

0.935

0.638

0.610

K-4-2

2

0.934

0.621

0.553

K-3-2

2

0.916

0.620

0.523

Q-J-10

10

1.228

0.948

0.974

Q-J-9

9

1.245

0.814

0.846

Q-J-8

8

1.262

0.732

0.765

Q-J-7

7

1.273

0.662

0.692

Q-J-6

6

1.274

0.648

0.618

Q-J-5

5

1.275

0.628

0.602

Q-J-4

4

1.274

0.608

0.584

Q-J-3

3

1.269

0.591

0.567

Q-J-2

2

1.265

0.573

0.550

Q-10-9

9

1.192

0.814

0.867

Q-10-8

8

1.204

0.730

0.788

Q-10-7

7

1.224

0.665

0.720

Q-10-6

6

1.219

0.648

0.633

Q-10-5

5

1.221

0.631

0.568

Q-10-4

4

1.219

0.608

0.551

Q-10-3

3

1.216

0.590

0.537

Q-10-2

2

1.213

0.576

0.523

Q-9-8

8

1.062

0.724

0.789

Q-9-7

7

1.076

0.658

0.739

Q-9-6

6

1.078

0.645

0.661

Q-9-5

5

1.077

0.630

0.587

Q-9-4

4

1.078

0.611

0.517

Q-9-3

3

1.074

0.590

0.504

Q-9-2

2

1.072

0.573

0.491

Q-8-7

7

0.986

0.655

0.766

Q-8-6

6

0.988

0.641

0.705

Q-8-5

5

0.987

0.626

0.632

Q-8-4

4

0.991

0.610

0.555

Q-8-3

3

0.990

0.593

0.488

Q-8-2

2

0.986

0.574

0.478

Q-7-6

6

0.916

0.639

0.736

Q-7-5

5

0.916

0.625

0.681

Q-7-4

4

0.917

0.605

0.604

Q-7-3

3

0.916

0.589

0.526

Q-7-2

2

0.916

0.574

0.465

Q-6-5

5

0.902

0.625

0.710

Q-6-4

4

0.902

0.604

0.651

Q-6-3

3

0.903

0.589

0.579

Q-6-2

2

0.904

0.573

0.504

Q-5-4

4

0.887

0.599

0.698

Q-5-3

3

0.885

0.583

0.643

Q-5-2

2

0.889

0.571

0.573

Q-4-3

3

0.872

0.584

0.608

Q-4-2

2

0.870

0.568

0.555

Q-3-2

2

0.855

0.568

0.525

J-10-9

9

1.165

0.803

0.850

J-10-8

8

1.183

0.723

0.773

J-10-7

7

1.197

0.654

0.704

J-10-6

6

1.214

0.599

0.641

J-10-5

5

1.213

0.585

0.566

J-10-4

4

1.210

0.564

0.551

J-10-3

3

1.209

0.547

0.535

J-10-2

2

1.206

0.533

0.521

J-9-8

8

1.046

0.721

0.772

J-9-7

7

1.062

0.650

0.725

J-9-6

6

1.077

0.596

0.666

J-9-5

5

1.078

0.585

0.586

J-9-4

4

1.075

0.566

0.516

J-9-3

3

1.077

0.548

0.504

J-9-2

2

1.075

0.534

0.491

J-8-7

7

0.976

0.650

0.753

J-8-6

6

0.992

0.593

0.710

J-8-5

5

0.990

0.581

0.632

J-8-4

4

0.994

0.566

0.553

J-8-3

3

0.990

0.549

0.485

J-8-2

2

0.989

0.533

0.476

J-7-6

6

0.914

0.591

0.740

J-7-5

5

0.914

0.581

0.681

J-7-4

4

0.916

0.563

0.603

J-7-3

3

0.915

0.548

0.526

J-7-2

2

0.915

0.536

0.465

J-6-5

5

0.848

0.577

0.716

J-6-4

4

0.851

0.562

0.655

J-6-3

3

0.850

0.546

0.582

J-6-2

2

0.853

0.534

0.507

J-5-4

4

0.839

0.559

0.698

J-5-3

3

0.839

0.541

0.641

J-5-2

2

0.840

0.531

0.572

J-4-3

3

0.822

0.542

0.609

J-4-2

2

0.823

0.530

0.555

J-3-2

2

0.810

0.530

0.524

10-9-8

8

1.050

0.735

0.756

10-9-7

7

1.066

0.667

0.706

10-9-6

6

1.083

0.604

0.649

10-9-5

5

1.099

0.553

0.592

10-9-4

4

1.096

0.538

0.513

10-9-3

3

1.097

0.521

0.501

10-9-2

2

1.093

0.508

0.488

10-8-7

7

0.983

0.665

0.733

10-8-6

6

0.999

0.604

0.693

10-8-5

5

1.016

0.553

0.638

10-8-4

4

1.014

0.538

0.549

10-8-3

3

1.016

0.524

0.486

10-8-2

2

1.014

0.507

0.474

10-7-6

6

0.922

0.602

0.724

10-7-5

5

0.937

0.551

0.685

10-7-4

4

0.937

0.536

0.599

10-7-3

3

0.937

0.523

0.523

10-7-2

2

0.939

0.511

0.462

10-6-5

5

0.866

0.549

0.721

10-6-4

4

0.864

0.533

0.653

10-6-3

3

0.866

0.520

0.581

10-6-2

2

0.868

0.510

0.505

10-5-4

4

0.803

0.531

0.705

10-5-3

3

0.804

0.519

0.645

10-5-2

2

0.807

0.508

0.575

10-4-3

3

0.792

0.518

0.609

10-4-2

2

0.794

0.506

0.555

10-3-2

2

0.779

0.506

0.525

9-8-7

7

0.959

0.671

0.715

9-8-6

6

0.975

0.614

0.673

9-8-5

5

0.990

0.556

0.619

9-8-4

4

1.006

0.500

0.554

9-8-3

3

1.006

0.488

0.481

9-8-2

2

1.003

0.474

0.471

9-7-6

6

0.918

0.611

0.707

9-7-5

5

0.937

0.554

0.668

9-7-4

4

0.951

0.497

0.605

9-7-3

3

0.953

0.486

0.520

9-7-2

2

0.952

0.478

0.458

9-6-5

5

0.869

0.553

0.704

9-6-4

4

0.883

0.497

0.656

9-6-3

3

0.886

0.486

0.578

9-6-2

2

0.887

0.475

0.503

9-5-4

4

0.817

0.495

0.707

9-5-3

3

0.817

0.485

0.645

9-5-2

2

0.818

0.472

0.571

9-4-3

3

0.754

0.485

0.616

9-4-2

2

0.755

0.476

0.556

9-3-2

2

0.744

0.476

0.524

8-7-6

6

0.927

0.643

0.690

8-7-5

5

0.941

0.587

0.649

8-7-4

4

0.957

0.525

0.589

8-7-3

3

0.973

0.472

0.525

8-7-2

2

0.973

0.464

0.456

8-6-5

5

0.892

0.587

0.688

8-6-4

4

0.907

0.522

0.639

8-6-3

3

0.923

0.468

0.582

8-6-2

2

0.925

0.463

0.502

8-5-4

4

0.841

0.520

0.692

8-5-3

3

0.859

0.467

0.647

8-5-2

2

0.860

0.462

0.569

8-4-3

3

0.786

0.468

0.621

8-4-2

2

0.787

0.463

0.556

8-3-2

2

0.724

0.463

0.531

7-6-5

5

0.899

0.618

0.668

7-6-4

4

0.915

0.559

0.622

7-6-3

3

0.933

0.498

0.565

7-6-2

2

0.947

0.449

0.505

7-5-4

4

0.868

0.557

0.675

7-5-3

3

0.885

0.493

0.630

7-5-2

2

0.902

0.447

0.574

7-4-3

3

0.814

0.495

0.603

7-4-2

2

0.831

0.449

0.561

7-3-2

2

0.758

0.448

0.533

6-5-4

4

0.881

0.591

0.658

6-5-3

3

0.897

0.536

0.611

6-5-2

2

0.916

0.477

0.557

6-4-3

3

0.841

0.537

0.585

6-4-2

2

0.860

0.479

0.543

6-3-2

2

0.793

0.480

0.518

5-4-3

3

0.866

0.582

0.562

5-4-2

2

0.884

0.528

0.519

5-3-2

2

0.829

0.530

0.497

Power Ratings

The following tables show my power ratings for all hands the player might play, assuming he always plays the two cards with the greatest expected value, as shown in the tables above. Assuming that, some situations will never be played, like unsuited K-6, where the discard is suited to the K or 6. I inflated the expected values by 36.9, so that the best possible hand, A-A discarding a non-ace, had a value of 100. Of course, the actual power ratings will depend slightly on the rank of the discard, so the values seen here are a weighted average.

The following table shows the power rating of holding a pair. The columns are divided according to whether there is a rank penalty (being dealt a three of a kind), a suit penalty (a singleton is suited to a card in the pair, lowering the chance of making a flush, and no penalty card at all.

The following table shows the power ratings of holding any combination of two suited cards, where the discard is of the same suit. In other words, being dealt a three-card flush.

The following table shows the power ratings of holding any combination of two suited cards, where the discard is of a different suit.

The following table shows the power ratings of holding any combination of two off-suit cards, where the discard is suited to one of them, lowering the chances of making a flush.

The following table shows the power ratings of holding any combination of two off-suit cards, where the discard is of a different suit to both of them. In other words, being dealt a "rainbow," which is three different suits.

Methodology

The expected values and strategy in this page were the result of a random simulation. To determine the strategy, I first developed a basic strategy for playing against five psychic opponents, who always held the two cards that would maximize the value of the final hand. I then had all five opponents play this anti-psychic strategy and developed a new optimal strategy to defeat that. I then repeated this process four more times, until the strategy found a Nash equilibrium that couldn't be improved upon. The final numbers are based on a simulation of 6,610,500,000 rounds.
Written by: Michael Shackleford